Aligning method

ABSTRACT

An aligning method suitably usable in a semiconductor device manufacturing exposure apparatus of step-and-repeat type, for sequentially positioning regions on a wafer to an exposure position. In one preferred form, the marks provided on selected regions of the wafer are detected to obtain corresponding mark signals and then respective positional data related to the positions or positional errors of the selected regions are measured, on the basis of the mark signals. Then, the reliability of each measured positional data of a corresponding selected region is detected, on the basis of the state of a corresponding mark signal or the state of that measured positional data and by using fuzzy reasoning, for example. Corrected positional data related to the disposition of all the regions on the wafer is then prepared by using the measured positional data of the selected regions, wherein, for preparation of the corrected positional data, each measured positional data is weighted in accordance with the detected reliability thereof such that measured positional data having higher reliability is more influential to determine the corrected positional data. For sequential positioning of the regions on the wafer to the exposure position, the wafer movement is controlled on the basis of the prepared corrected positional data, whereby high-precision alignment of each region is assured.

This application is a divisional of application Ser. No. 08/139,059,filed Oct. 21, 1993, pending, which application is a continuation ofapplication Ser. No. 08/040,081, filed Mar. 30, 1993, abandoned, whichapplication is a continuation of application Ser. No. 07/520,248, filedMay 7, 1990, abandoned.

FIELD OF THE INVENTION AND RELATED ART

This invention relates to an aligning method for correctly positioningdifferent portions of a workpiece to a desired site in sequence. Moreparticularly, the invention is concerned with an aligning method usablein a semiconductor device manufacturing step-and-repeat type exposureapparatus, for measuring positions or positional errors related to someof the shot areas on a semiconductor wafer, then for determining fromthe results the disposition of all of the shot areas of the wafer andfor correctly positioning these shot areas of the wafer in sequence to asite related to a reticle (photomask) on the basis of the thusdetermined shot disposition.

As an aligning method usable in a semiconductor device manufacturingstep-and-repeat type exposure apparatus (stepper), for correctlypositioning different shot areas of a wafer to a site related to areticle (photomask), a proposal has been made in Japanese Laid-OpenPatent Application, Laid-Open No. Sho 63-232321 filed in the name of theassignee of the subject application. According to this proposal,positions or positional errors related to some shot areas on asemiconductor wafer are measured and, by using the results, thedisposition of all the shot areas on the wafer is determined. Then, byusing the thus determined shot disposition, the wafer is moved stepwiseso as to correctly position each shot area of the wafer with respect toa site related to a reticle (photomask), in a predetermined order.

SUMMARY OF THE INVENTION

More specifically, in the aligning method according to this proposal,any extraordinary value or values included in the measured position dataare rejected and, from the measured positional data related to some shotareas, the disposition of all the shot areas on the wafer is determinedby using a statistical method, for example. However, during thisdetermination, all the measured positional data are processed on anassumption that they have the same reliability. Accordingly, in thisaligning method, those measured positional data having high reliabilityand those measured data having lower reliability, have the sameinfluence upon determination of the shot disposition (chip disposition).

Such a difference in reliability of the measured data may be disregardedfrom the standpoint of conventionally required alignment precision.However, in consideration of increasing resolving power of a stepperwhich requires corresponding enhancement of the alignment precision,such a difference in reliability of the measured data should beconsidered.

In this respect, it is accordingly a primary object of the presentinvention to provide an improved aligning method which ensures furtherenhancement of the alignment precision.

It is another object of the present invention to provide an aligningmethod usable, for example, in a semiconductor device manufacturingstep-and-repeat type exposure apparatus, for measuring positions orpositional errors related to some shot areas on a semiconductor wafer,then for determining from the results the disposition of all the shotareas of the wafer and for correctly positioning each shot area of thewafer to a site related to a reticle on the basis of the thus determinedshot disposition, with enhanced alignment precision.

In accordance with an aspect of the present invention, to achieve atleast one of these objects, the reliability of each measured positionaldata is determined on the basis of the state of each mark detectionsignal (mark signal) obtained as a result of detection of each markprovided in each shot area, or on the basis of the state of eachmeasured positional data related to each shot area. Then, from valuesrelated to these measured positional data having been weighted inaccordance with the determined reliability, the disposition (correctedposition data) of all the shot areas of a wafer (workpiece) isdetermined. This means that those measured position data having high orhigher reliability, have stronger influence upon determination of theshot disposition and, therefore, the alignment precision can beenhanced.

In accordance with an aspect of the present invention, the reliabilityof each measured positional data is determined on the basis of fuzzyreasoning, from the states of mark signals obtained from alignment marksof shot areas or, alternatively, from the states of measured positionaldata of the shot areas. The fuzzy reasoning is a best method fordetermination of the reliability of each measured positional data byusing plural conditional propositions.

In accordance with another aspect of the present invention, thedetermined shot disposition may be represented by an approximationfunction and, on that occasion, the square or absolute value of adifference (hereinafter "remainder") between the actual position of eachshot area as represented by a corresponding measured positional data andthe position of that shot area as represented by the approximationfunction, may be weighted in accordance with the reliability of thecorresponding measured positional data, and the approximation functionmay be determined so that the sum of the weighted remainders is reducedto a minimum. This makes it possible to determine the approximationfunction so as to ensure that those measured positional data having highor higher reliability are more influential than those measuredpositional data having low or lower reliability.

These and other objects, features and advantages of the presentinvention will become more apparent upon a consideration of thefollowing description of the preferred embodiments of the presentinvention taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a perspective view, schematically showing a semiconductordevice manufacturing step-and-repeat type exposure apparatus accordingto an embodiment of the present invention.

FIG. 2 is a schematic representation, showing details of a control unitused in the FIG. 1 embodiment.

FIG. 3A is a plan view, schematically showing a wafer usable in the FIG.1 embodiment.

FIG. 3B is a detail of that plan view.

FIG. 4 is a schematic representation, showing the state of marks asimaged on an image pickup surface of an image pickup device.

FIG. 5(a) is a schematic illustration, showing an idealistic mark image.

FIG. 5(b) is a schematic illustration showing waveforms of mark signalsrelated thereto.

FIGS. 6(a) through 6(f) are schematic representations, showing atemplate for a mark signal as well as the template match degree.

FIGS. 7(a) through 7(c) are schematic representations, showing a marksignal when a mark bears a noise as well as the template match degree inthat case.

FIGS. 8(a) through 8(c) are schematic representations, showing a marksignal when a mark is covered by a non-uniform resist as well as thetemplate match degree in that case.

FIGS. 9(a) through 9(c) are schematic representations, showing a marksignal when a mark has asymmetrical edge taper angles as well as thetemplate match degree in that case.

FIGS. 10(a) and 10(b) are schematic representations, showing marksignals when a mark is deformed.

FIGS. 11(a) and 11(b) are schematic representations, showing marksignals when the intensity of mark illuminating light is weak.

FIGS. 12(a) to 12(c) are schematic representations, showing idealisticmark measurement as well as variance in the measured values of the casesof FIGS. 10(a) and 10(b) and 11(a) and 11(b).

FIGS. 13A and 13B are schematic representations, showing the manner ofvariation in the measured positional deviation on an occasion when amark is rotated.

FIG. 14 is a flow chart showing the sequence of an aligning operationaccording to the FIG. 1 embodiment.

FIG. 15 is a block diagram, showing details of a major part of the flowchart of FIG. 14.

FIG. 16 is a schematic representation, showing the relationship amongposition vectors used in the explanation of the FIG. 1 embodiment.

FIG. 17 is a perspective view, schematically showing a major part of asemiconductor device manufacturing step-and-repeat type exposureapparatus according to another embodiment of the present invention.

FIG. 18 is a flow chart showing another example of the sequence of analigning operation.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring first to FIG. 1, which shows a semiconductor devicemanufacturing step-and-repeat type exposure apparatus according to anembodiment of the present invention, denoted at RT is a reticle having apattern PT for manufacture of semiconductor devices; at WF is asemiconductor wafer having a number of shot areas (chips) SH formedthereon; at LN is a projection lens system for projecting in a reducedscale the pattern PT of the reticle RT onto one shot area SH of thewafer WF at a time; at CU is a control unit for controlling the stepperas a whole; and at CS is a console to be used for supplying necessaryinformation such as alignment data, exposure data and the like into thecontrol unit CU.

The control unit CU includes computers, memories, an image processingdevice, an X-Y stage control device and so on. Also, there is providedan image pickup device CM and, in order to obtain the amount ofpositional deviation of a mark being examined as well as acharacteristic parameter (reliability) related thereto from a videosignal of the image pickup device CM, as shown in FIG. 2 there areprovided an analog-to-digital converting device (hereinafter A/Dconverting device) 21 for quantizing the video signals from the imagepickup device CM; an integrating device 22 for integrating the quantizedvideo signals from the A/D converting device 21, with respect to apredetermined direction; a position detecting device 23 for detectingthe positional deviation of the mark on the basis of an integratedsignal from the integrating device 22; and a characteristic parameterextracting device 24 for extracting the characteristic parameter(reliability) of the positional deviation as detected by the positiondetecting device 23. The structure will be described later in detail.

The reticle RT is attracted to and held by a reticle stage RS which ismovable in X, Y and θ directions in accordance with an instructionsignal from the control unit CU. The reticle RT is provided with reticlealignment marks RAMR and RAML to be used to position the reticle RT intoa predetermined positional relationship with the projection lens systemLN, as well as reticle marks RMR and RML to be used for detection of thepositional relationship between the reticle RT and each shot area SH ofthe wafer WF.

Reticle setting marks RSMR and RSML are formed on a stationary memberfixed to the barrel of the projection lens system LN, so that thesesetting marks are in a predetermined positional relationship with theprojection lens system LN. For correct positioning of the reticle RTwith respect to the projection lens system LN, an image of the set ofmarks RAMR and RSMR and an image of the set of marks RAML and RSML aresuperposed one upon another on the image pickup device CM and, then, thecontrol unit CU operates to move the reticle stage RS so as to reducethe relative positional deviation between them, detected from the videosignal, to a predetermined tolerance.

The wafer WF is attracted to and held by a wafer stage WS. The waferstage WS is operable to displace the wafer WF relative to an X-Y stageXYS, in the Z and θ directions. Denoted at MX and MY are motors formoving the X-Y stage XYS in the X and Y directions; at MRX and MRY aremirrors fixedly secured to the X-Y stage XYS, and at IFX and IFY arelaser interferometers. By means of these laser interferometers IFX andIFY as well as the mirrors MRX and MRY, the position in X-Y coordinatesof the X-Y stage XYS for moving the wafer WF in the X and Y directionscan be monitored. Further, by means of the motors MX and MY, the X-Ystage can be moved to a position designated by the control unit CU. Evenafter completion of the movement, the control unit CU operates to holdthe X-Y stage XYS at the designated position on the basis of the outputsof the laser interferometers IFX and IFY.

FIG. 3A and 3B show details of the wafer WF. Through the precedingexposure process or processes, a number of patterns (shot areas SH) areformed on the wafer WF which patterns are arrayed approximately alongthe X and Y directions. Further, wafer alignment marks WAML and WAMR areformed on the wafer. In each shot area SH, wafer marks WML and WMR areformed with an interspace MS. It is to be noted here that designpositions of the wafer alignment marks WAML and WAMR, design positionsof the individual shot areas SH and design positions of the wafer marksWML and WMR of each shot area SH, with respect to the X-Y coordinates asthe wafer WF is attracted to and held by the wafer stage WS (FIG. 1), aswell as the design value of the mark interspace MS, are inputted inpreparation into the control unit CU from the console CS.

In FIG. 3A, those shot areas as hatched by oblique lines or verticallines are the sample shot areas to be selected as the subject ofmeasurement during the positional deviation measurement for alignment ofeach shot area SH of the wafer WF with the reticle RT. Hereinafter,those shot areas as hatched by oblique lines will be referred to as"preparatory sample shot areas" (SS1, SS3, SS5 and SS7) while, on theother hand, those shot areas as hatched by oblique lines or verticallines will be referred to as "sample shot areas" (SS1-SS8), fordistinction from the other shot areas. Also, the sites of these sampleshot areas SS1-SS8 have been inputted into the control unit CU from theconsole CS, like the case of the marks as described.

Referring back to FIG. 1, denoted at OS is an off-axis scope forobserving the images of the wafer alignment marks WAML and WAMR of thewafer WF, for detection of their positions in the X-Y coordinates. Theoff-axis scope OS is securedly fixed to the projection lens system LN sothat a predetermined positional relationship is maintained therebetween.Denoted at IL is an illumination device for illuminating the reticle RTwith light of a predetermined printing wavelength or wavelengths whenthe pattern PT of the reticle RT is to be printed on a shot area SH ofthe wafer WF through the projection lens system. Shutter SHT is providedto control the amount of exposure for the pattern printing. Theillumination device and the shutter operate in accordance with theinstruction signals from the control unit CU.

Denoted at LS is a laser source for producing laser light of awavelength substantially the same as the printing wavelength. When, fordetection of relative positional deviation between a certain wafer shotarea SH and the pattern PT of the reticle RT through the projection lenssystem, the set of reticle mark RML and wafer mark WML and the set ofreticle mark RMR and wafer mark WMR are to be imaged superposedly uponthe image pickup device CM, the laser light from the laser source LS isused to illuminate these marks. The laser light from the laser source LSis once diffused and averaged by a diffusing plate DP and, thereafter,it is used to illuminate these marks. Denoted at LSH is a shutter whichoperates, for example, when the X-Y stage XYS is being moved stepwise,to block the laser light from the laser source LS so that it does notimpinge on the wafer WF.

Next, the manner of detecting any positional deviation with thestructure described above, will be explained. In the followingexplanation, the right-hand side of the apparatus as it is viewed in thedirection of an arrow of FIG. 1 will be called "right" and the left-handside of the apparatus of FIG. 1 will be called "left".

The laser light emitted from the laser source LS is diffused by thediffusing plate DP and, thereafter, it is scanningly deflected by apolygonal mirror PM. After this, the light is transformed by an f-θ lensFθ into a constant-speed scanning light which in turn passes through abeam splitter BS and, then, is divided leftwardly and rightwardly by aroof prism DAP. The leftward split laser light is reflected by aright-hand objective mirror AMR so that it is projected onto a zone ofthe reticle RT including the reticle mark RMR, from above the reticleRT. The laser light passing through the reticle RT goes through thereduction projection lens system LN by which it is projected onto a zoneof a particular shot area, including the right-hand wafer mark WMR.Reflection light from the zone including the wafer mark WMR goesbackwardly along its oncoming path and, after passing the projectionlens system LN and the zone including the reticle mark RNR, it impingeson the roof prism DAP. Similarly, the laser light split rightwardly bythe roof prism DAP is reflected by a left-hand objective mirror AML tobe projected onto a zone of the reticle including the reticle mark RMLand, thereafter, along a similar path, reflection light from a zone ofthe wafer including the wafer mark WML comes back to the roof prism DAP.The left-hand and right-hand laser lights are combined at the roof prismDAP, and the combined light goes through the beam splitter BS and, afterbeing magnified by an erector EL, it is imaged on the image pickupsurface of the image pickup device CM to form images such as shown inFIG. 4. The imaging light from the wafer marks WML and WMR, to be imagedupon the image pickup device, is diffused by the erector EL so thatthese marks are imaged at an enlarging magnification of ×65. Also, theimage pickup device CM comprises a photoelectric converting device suchas an ITV camera or a two-dimensional (area) image sensor, for example,and is adapted to convert the received images of the reticle marks RSLand RSR and the wafer marks WML and WMR into two-dimensional electricsignals.

FIG. 4 illustrates reticle marks RSL and RSR as well as wafer marks WSLand WSR as imaged upon the image pickup device CM. In this Figure, thereticle marks RML and RMR and the wafer marks WML and WMR, described inthe foregoing, are defined in greater detail. Namely, in FIG. 4, thereticle mark RML is depicted by marks RML_(X) and RML_(Y) ; the reticlemark RMR is depicted by marks RMR_(X) and RMR_(Y) ; the wafer marks WMLis depicted by marks WML_(X) and WML_(Y) ; and the wafer mark WMR isdepicted by marks WMR_(X) and WMR_(Y). The left half of FIG. 4illustrates the images of the left-hand marks WML_(X) and WML_(Y) of ashot area SH and the right-hand marks RML_(X) and RML_(Y) of the reticleRT, while the right half of FIG. 4 illustrates the images of theright-hand marks WMR_(X) and WMR_(Y) of the shot area SH and the imagesof the left-hand marks RMR_(X) and RMR_(Y) of the reticle RT. The reasonwhy the images of the reticle marks RML_(X), RML_(Y), RMR_(X) andRMR_(Y) are dark, is that the reticle RT is backside-illuminated withthe reflection light from the wafer WF and the transmitted light fromthe reticle is picked up by the image pickup device CM.

The image converted into a two-dimensional electric signal by the imagepickup device is digitalized (e.g. binary-coded) by the A/D convertingdevice 21 (FIG. 2) and is stored into an image memory having x-yaddresses corresponding to the positions of picture elements of theimage pickup surface. The content of the image memorized into the imagememory corresponds to that having x addresses (coordinate) designated inthe horizontal direction in FIG. 4 and y addresses (coordinate)designated in the vertical direction in FIG. 4.

Deviation measurement is performed with regard to each of the four setsof mark images of FIG. 4, independently of the others. Morespecifically, from the difference in position on the image surfacebetween the reticle mark RML_(X) and the wafer mark WML_(X), theleft-hand viewfield deviation D_(lx) in the X direction through theobjective mirror AML is detected; similarly from the reticle markRML_(Y) and the wafer mark WML_(Y), the left-hand viewfield deviationD_(ly) in the Y direction is detected; from the reticle marks RMR_(X)and the wafer mark WMR_(X), the right-hand viewfield deviation D_(rx) inthe X direction through the objective mirror AMR is detected; and fromthe reticle mark RMR_(Y) and the wafer mark WMR_(Y), the right-handviewfield deviation D_(ry) in the Y direction is detected. Since themeasurement of these deviations can be made essentially in the samemanner, although the measured values in the X-Y coordinates may bedifferent, description will be made only of an example of themeasurement in the left-hand viewfield in the X direction.

FIG. 5, part (a) shows the upper left set of marks RML_(X) and WML_(X)of FIG. 4. In superposition of the pattern PT of the reticle RT upon thepattern in the shot area SH, the mating marks as described hereinbeforeare so designed that the relative positional deviation becomes null whencorrect pattern superposition can be done. Namely, in FIG. 5(a), if theposition of the left mark component of the reticle mark RML_(X), on theimage pickup surface, is denoted by PRL, the position of the right markcomponent thereof on the image pickup surface is denoted by PRR and theposition of the wafer mark WML_(X) on the image pickup surface isdenoted by PWM, then deviation D_(lx) can be expressed by:

    D.sub.lx =PMW-(PRL+PRR)/2

Next, description will be made of the method of calculating thesepositions PRL, PRR and PWM. Reference characters W_(k) (k=1-n), in FIG.5, part (a), denote two-dimensional windows set on the image pickupsurface. In each of these windows W_(k), the integrating device 22 shownin FIG. 2 serves to integrate the picture element values from the A/Dconverting device 21 with respect to a direction (Y direction in thiscase) perpendicular to the direction (X direction in this case) withrespect to which the positional deviation is to be detected. By this,one-dimensional integrated waveforms S_(k) (x) are provided. When thevalue of picture element data on the image memory is denoted by P(X,Y)and the range of the window W_(k) in the Y direction is denoted byY_(k1) ≦Y≦Y_(k2), then S_(k) (x) is expressed as follows: ##EQU1##Actually, as illustrated in FIG. 5(a), windows W_(k) of a number n areset and, with regard to each window, projected and integrated waveformssuch as illustrated in FIG. 5(b), are obtained. In the image as pickedup, the edge signal portions of the reticle mark RML_(X) and the wafermark WML_(X) have largely changing contrast as compared with the otherportions. As a result, in the integrated waveform S_(k) (x), thecontrast in the direction (X direction) perpendicular to the directionof integration is emphasized and the signal-to-noise ratio (S/N ratio)is enhanced. Accordingly, in these signal portions, a towering peak or afall is observed.

The position detecting device 23 of FIG. 2 serves to detect the markpositions PRL, PRR and PWM from the above-described integrated waveformsS_(k) (x). In this position detecting device 23, the same processing isperformed to the integrated waveforms S₁ (x)-S_(n) (x) of FIG. 5(b). Thefollowing explanation will be made of an example of an arbitraryintegrated waveform S(x). The mark position detecting operation isdivided into a process of detecting the reticle mark positions PRL andPRR and a process of detecting the wafer mark position PWM. Also, eachmark detecting process is divided into a process of determining anapproximate position and a process of determining an exact position.

For each of the wafer mark position detection and the reticle markposition detection, the approximate position determining process uses atemplate matching method. First, detection of the position PWM of thewafer mark WML_(X) will be explained. When an idealistic waveformobtained by the integration is such as depicted at S(x) in part (a) ofFIG. 6 and the template is such as at P(x) in part (b) of FIG. 6, then,according to the matching evaluation equation given below, the matchdegree E(x_(k)) at an arbitrary point x_(k) is provided. ##EQU2##

The parameters a and b in the above equation mean the effective range ofthe template and are used to adjust the characteristics of the templatein accordance with the characteristics of S(x). The value of matchdegree E(x_(k)) with respect to the arbitrary point x_(k) has a peak atthe approximate position of the wafer mark WML, such as illustrated inFIG. 6(c). The x_(k) coordinate value at which the match degree E(x_(k))shows a peak is denoted by x_(p), and this peak value is taken as a peakmatch degree E(x_(p)). Actually, depending on the semiconductor devicemanufacturing process or the relationship with the resist film thicknessor the like, the integrated waveform is not always such as depicted atS(x). In consideration thereof, actually a few types of templates areused to execute similar processings to calculate corresponding matchdegrees, and a maximum one of them is adopted. Representative types oftemplates other than those shown in FIG. 6(b) are illustrated in FIG. 6,(d)-(f). The exact mark position is determined by executing, with regardto the adopted match degree function E(x_(k)), a gravity centercalculation at a few points about the position x_(p). Alternatively,E(x_(k)) may be curve-approximated and the exact position may bedetermined from a peak value of the approximation curve.

Coarse detection of positions PRL and PRR of the mark components of thereticle mark RML_(X) comprises similar template matching operations.Particularly, by using the fact that the interspacing between tworeticle mark components (see FIG. 4) has an approximately constantvalue, template parameters (-b-a) and (a-b) are set with regularintervals. Precise detection of the positions PRL and PRR is performedby calculating the positions of two reticle mark components, asdetermined by the template matching, from the center position of the tworeticle mark components and, then, by executing gravity centercalculation of the integrated waveform S(x) around the approximateposition with respect to which the left and right reticle markcomponents have been calculated.

In this manner, for each of the windows W_(k), the position detectingdevice 23 determines the reticle mark positions PRL_(k) and PRR_(k) andthe wafer mark position PWM_(k) shown in FIG. 5(b) and, thereafter, foreach window W_(k) it determines the positional deviation D_(lxk) betweenthe reticle mark RML_(X) and the wafer mark WML_(X) by computation usingthe above-described equation. Then, an average of positional deviationsD_(lxk) obtained with regard to the respective windows W_(k) is detectedas, in accordance with the equation to be set forth below, thepositional deviation D_(lx) between the reticle mark RML_(X) and thewafer mark WML_(X). Also, by similar processing, positional deviationD_(ly) is detected from positional deviations D_(lyk) between thereticle mark RML_(Y) and the wafer mark WML_(Y) with regard to therespective windows W_(k) ; positional deviation D_(rx) is detected frompositional deviations D_(rxk) between the reticle mark RMR_(X) and thewafer mark WMR_(X) with regard to the respective windows W_(k) ; andpositional deviation D_(ry) is detected from positional deviationsD_(ryk) between the reticle mark RMR_(Y) and the wafer mark WMR_(Y) withregard to the respective windows W_(k). ##EQU3##

The characteristic parameter extracting device 24 of FIG. 2 serves toobtain an evaluated quantity for the certainty of the detected markposition, namely, for the certainty (reliability) of each of thepositional deviations D_(lx), D_(ly), D_(rx) and D_(ry) as determined bythe position detecting device 23. More specifically, correspondingly tothe detected positional deviations D_(lx), D_(ly), D_(rx) and D_(ry),the characteristic parameter extracting device 24 operates: (1) todetect averages P_(lx), P_(ly), P_(rx) and P_(ry) of the peak matchdegrees E_(lxk) (Xp), E_(lyk) (Xp), E_(rxk) (Xp) and E_(ryk) (Xp) in therespective windows W_(k), in accordance with the following equations:##EQU4## Also, it operates (2) to detect variances σ_(lx), σ_(yl),σ_(rx) and σ_(ry) of the positional deviations D_(lxk), D_(lyk), D_(rxk)and D_(ryk) in the respective windows W_(k), in accordance with thefollowing equations: ##EQU5## Further, it operates (3) to detect errorsΔRS_(ilx), ΔRS_(ily), ΔRS_(irx) and ΔRS_(iry) between the sample shotareas SSi of the averages RS_(lx), RS_(ly), RS_(rx) and RS_(ry) (seeFIG. 4) of the intervals RS_(lxk), RS_(lyk), RS_(ryk) and RS_(ryk) ofthe reticle mark components for the respective windows W_(k), inaccordance with the following equations: ##EQU6## wherein i=1-n, and nis the number of sample shot areas selected as the subject ofmeasurement. Each of the intervals RS_(lxk), RS_(lyk), RS_(rxk) andRS_(ryk) is determined by the difference between the positions PRL_(k)and PRR_(k) of the reticle mark components in corresponding windowW_(k).

Also, the characteristic parameter extracting device 24 further operates(4) to detect, as evaluated quantities, the shot (chip) magnificationerrors ΔMag_(i) among the sample shot areas SSi in accordance with thefollowing equation, with a definition that the shot magnificationMag_(i) of the i-th sample shot area is the difference between thepositional deviations D_(lx) and D_(rx) as detected with regard to thatshot area: ##EQU7## Also, it operates (5) to detect the shot (chip)rotational angle errors Δθi among the sample shot areas SSi inaccordance with the following equation, with a definition that the shotrotational angle θi of the i-th sample shot area is the differencebetween the positional deviations D_(ly) and D_(ry) as detected withregard to that shot area: ##EQU8##

Next, by using the evaluated quantities as set in the above-describeditems (1)-(5), the characteristic parameter extracting device 24evaluates the certainty of the positional deviations D_(ilx), D_(ily),D_(irx) and D_(iry) at the sample shot areas SSi detected by theposition detecting device 23. Before explaining this, the meaning of theevaluation quantities as set in items (1)-(5) will be explained briefly.

As regards item (1), by way of example, description will be made of acase wherein noise is present on a mark shown in FIGS. 7(a) through 7(c)a case wherein non-uniformness of applied resist is present on a wafermark shown in FIGS. 8(a) through 8(c) and a case where edges of a wafermark shown in FIGS. 9(a) through 9(c) have asymmetrical taper angles.

FIG. 7, part (a), shows the wafer mark WML_(X) as imaged on the imagepickup surface of the image pickup device CM. Denoted at DA are noisesresulting from foreign particles on the wafer mark WML_(X), at NO arerough-surface noises produced by the preceding wafer process, and at Sare interference fringe noises produced by the interference of laserlight from the light source LS. FIG. 7, part (b), shows an integratedwaveform S(x) corresponding to the mark, and FIG. 7(c) shows acorresponding peak match degree E(x_(k)). It is seen from theillustration that, in a case such as shown in FIG. 7(a), the position Xpshown in FIG. 7(c) is deviated from the position XEI as assumed underidealistic conditions such as depicted in FIG. 6, part (c). Also, thepeak match degree E(x_(k)) at that time has two peaks and, additionally,the peak degree E(x_(p)) is lower than the peak match degree EI asprovided under the idealistic conditions shown in FIG. 6(c).

Accordingly, in a case as that of FIG. 7(a), the certainty of thedetected mark position is low and the certainty is variable in relationto the peak match degree.

FIG. 8, part (a) shows the section of a wafer WF non-uniformness inapplication of a resist R is present on a wafer mark WML_(X). In a casesuch as illustrated, the integrated waveform S(x) to the wafer markWML_(X) has a distorted shape such as illustrated in FIG. 8, (b). Forsuch a distorted waveform S(x) and the matching degree E(x_(k)) of atemplate P(x) such as shown in part (b) of FIG. 6, there occursdistortion such as shown in FIG. 8, (c). Also, the peak matching degreeE(x_(p)) at this time is lower than the peak matching degree EI asprovided under idealistic conditions shown in FIG. 6(c), and thecertainty of the position x_(p) in FIG. 8(c) obtainable therefrom islow. The position x_(p) in FIG. 8(c) is deviated from the position XEIas assumed under the idealistic conditions shown in FIG. 6(c), due tothe distortion of the matching degree E(x_(k)).

Distortion of the integrated waveform S(x) results from the differencein thickness between the portions r1 and r2 of the resist R. Due to thisdifference the periodic change in intensity produced by the interferencebetween reflection light from the resist R surface and reflection lightfrom the wafer WF surface, as illuminated by the laser light (alignmentlight) from the light source LS, differs between the portions r1 and r2.For this reason, the waveform S(x) is asymmetrical. Such non-uniformnessin resist application easily occurs when a spinning coater is usedwherein a resist R material is dropped onto the surface of a rotatingwafer WF so that, with the centrifugal force, the resist R material isapplied to the whole surface of the wafer WF. Particularly, suchnon-uniformness is produced on a mark which is at the outercircumferential part of the wafer WF.

FIG. 9, part (a), shows the section of a wafer WF in a case wherein theedges e1 and e2 of a wafer mark WML_(X) have asymmetrical taper angles.Also, in this case, the integrated waveform S(x) of the wafer markWML_(X) has a deteriorated shape due to distortion and noise, as shownin FIG. 9(b). As a result, the matching degree E(k) with the templateP(x) shown in FIG. 6(b) has distortion and two peaks such as shown inFIG. 9(c), and the position x_(p) is detected with a deviation from theposition XEI shown in FIG. 6(c). Also, the peak matching degree E(x_(p))at this time is lower than the peak matching degree EI shown in FIG.6(c) and, therefore, the certainty of the detected position x_(p) islow. Deterioration of the waveform S(x) is because of the fact that, dueto the difference in taper angle (inclination) between the edges e1 ande2 of the wafer WF, non-uniformness arises in the application of theresist R or, alternatively, a difference is produced in the angle ofscattering of the alignment light at the edges e1 and e2 whichdifference results in a difference in intensity of the reflected light.

It will be understood from the foregoing that, by detecting the peakmatch degrees P_(ilx), P_(ily), P_(irx) and P_(iry) in the manner asdescribed in item (1), it is possible to evaluate the certainty ofcorresponding positional deviations D_(ilx), D_(ily), D_(irx) andD_(iry).

Item (2) will now be explained. Variations σ_(ilx), σ_(ily), σ_(irx) andσ_(iry) for the positional deviations D_(ilx), D_(ily), D_(irx) andD_(iry) of the i-th sample shot area SSi, each is a quantity thatrepresents the degree of measurement dispersion, for each window W_(k),of a deviation with respect to a certain set of measured marks. Clearly,it can be said to be an average of deviations, that is, the quantitythat represents the certainty of positional deviation detectable fromthe mark set. If, for example, a part of a wafer mark WML_(X) isdeformed or local noises NO are present thereon such as shown in FIG.10(a), the integrated waveform S_(k) (x) of each window W_(k) is locallydeformed such as shown in FIG. 10(b), whereby the deviation of thedetected mark position D from the true position O is large. In such acase, the histogram of deviation in each window W_(k) has an expandeddistribution, as shown in FIG. 12(b), as compared with the histogram ofdeviation obtainable from a set of marks placed under idealisticconditions as shown in FIG. 12(a). Therefore, the variance becomes largeand the deviation of the detected position D from the true position Obecomes large.

Also, in the case of a good-condition mark set shown in FIG. 11, part(a), if a sufficient S/N ratio is not obtainable because of aninsufficient quantity of alignment light from the light source LS, forexample, its integrated waveform S_(k) (x) is influenced by random noisesuch as shown in FIG. 11(b) and, therefore, there is a tendency that themark position detectable from the integrated waveform S_(k) (x) containslarge measurement dispersion as shown in FIG. 12(c) and, consequently,the variance of positional deviation becomes large. Also, it is seenthat, because a sufficient number n of samples of the window W_(k)cannot be used, the average of the detected positions contains an errorlarger than that of the average of the detected positions forgood-condition marks. Thus, in such case there is a tendency that thedetected mark position D is largely displaced from the true position Oand the certainty of the detected deviation is small.

Further, in a case when the rotational angle θ between the shot area SHand the reticle RT is large and the wafer mark WML_(X) is largelyinclined relative to the reticle mark RML_(X) such as shown in FIG. 13A,the amount of deviation is dependent upon the position of the windowW_(k) as illustrated in FIG. 13B and the variance is large even if theconditions of the marks are good. It is to be noted that, in place ofvariance, the windows W_(k) may be defined at regular intervals and aleast square error when the amount of deviation relative to the windowW_(k) position is rectilinearly approximated, may be detected. On thatoccasion, by using a known method of regression analysis such as, forexample, the method discussed in "Statistic Analysis", Taguchi andYokoyama, Japanese Standards Association, "Chapter 3, 3.4 Formula ofRegression Analysis and its Induction", the least square error min(Se)can be expressed in the following manner:

When the window position is x and the deviation is y, first the valuesof m and b in the following equation are determined so as to minimizethe remaining square sum Se which is represented by: ##EQU9##

Next, item (3) will be explained. The interval of the reticle markcomponents is the quantity as determined by the set value of the reticlemark, and it is clear that the variation in its measured values RS_(lx),RS_(ly), RS_(rx) and RS_(ry) for different sample shot areas isinfluenced by any variation in measurement or by those elements thatreduce the certainty of measurement, such as variation in opticalmagnification, for example. Therefore, errors ΔRS_(ilx), ΔRS_(ily),ΔRS_(irx) and ΔRS_(iry) in the reticle mark interval of all the sampleshot areas SSi, selected as the subject of measurement, with referenceto an average reticle mark interval of all the sample shot areas, alsoreflect the certainty of measurement.

With regard to items (4) and (5), clearly the shot magnification errorΔMag_(i) and the shot rotational angle error Δθi of each sample shotarea SSi selected as the subject of measurement, have a relation withthe certainty of the detected mark position of that shot area. If theshot magnification error and the shot rotational angle error are large,the certainty of the detected mark position of that shot area is low.

Referring back to the characteristic parameter extracting device 24,after calculation of the evaluating quantities having been describedwith reference to items (1)-(5), for each sample shot area SSi thecharacteristic parameter extracting device 24 determines the certainty(characteristic parameter) W_(ix) and W_(iy) of the detected positionaldeviation D_(ix) and D_(iy) from these evaluating quantities, on thebasis of the fuzzy reasoning. Here, ##EQU10##

With respect to the detected positional deviations (detected markpositions) of the evaluating quantities discussed in items (1)-(5),fourteen (14) types of conditional propositions (Pj→Qj) are set in thecharacteristic parameter extracting device 24 in the form of fuzzyreasoning, wherein Pj is an antecedent proposition and Qj is aconsequent proposition.

The conditional propositions (P1→Q1) to (P4→Q4) are concerned with theaverages P_(lx), P_(ly), P_(rx) and P_(ry) of the peak match degrees(hereinafter, each average will be referred to as "peak match degree")as discussed in item (1). More specifically:

1. The conditional proposition (P1→Q1) is such that, in the i-th sampleshot area, (P1) if the peak match degree P_(ilx) is low, (Q1) thecertainty W_(i1) of the detected positional position deviation D_(ilx)is low.

2. The conditional proposition (P2→Q2) is such that, in the i-th sampleshot area, (P2) if the peak match degree P_(ily) is low, (Q2) thecertainty W_(i2) of the detected positional deviation D_(ily) is low.

3. The conditional proposition (P3→Q3) is such that, in the i-th sampleshot area, (P3) if the peak match degree P_(irx) is low, (Q3) thecertainty W_(i3) of the detected positional deviation D_(irx) is low.

4. The conditional proposition (P4→Q4) is such that, in the i-th sampleshot area, (P4) if the peak match degree P_(iry) is low, (Q4) thecertainty W_(i4) of the detected positional deviation D_(iry) is low.

On the other hand, the conditional propositions (P5→Q5) to (P8→Q8) areconcerned with the variances σ_(lx), σ_(ly), σ_(rx) and σ_(ry) discussedin item (2). More specifically:

5. The conditional proposition (P5→Q5) is such that, in the i-th sampleshot area, (P5) if the variance σ_(ilx) is large, (Q5) the certaintyW_(i5) of the detected positional deviation D_(ilx) is low.

6. The conditional proposition (P6→Q6) is such that, in the i-th sampleshot area, (P6) if the variance σ_(ily) is large, (Q6) the certaintyW_(i6) of the detected positional deviation D_(ily) is low.

7. The conditional proposition (P7→Q7) is such that, in the i-th sampleshot area, (P7) if the variance σ_(irx) is large, (Q7) the certaintyW_(i7) of the detected positional deviation D_(irx) is low.

8. The conditional proposition (P8→Q8) is such that, in the i-th sampleshot area, (P8) if the variance σ_(iry) is large, (Q8) the certaintyW_(i8) of the detected positional deviation D_(iry) is low.

Further, the conditional propositions (P9→Q9) to (P12-Q12) are thoserelated to the reticle mark deviations ΔRS_(ilx), ΔRS_(ily), ΔRS_(irx)and ΔRS_(iry) discussed in item (3). More specifically:

9. The conditional proposition (P9→Q9) is such that, in the i-th sampleshot area, (P9) if the reticle mark deviation ΔRS_(ilx) is not equal tozero (=0), (Q9) the certainty W_(i9) of the detected positionaldeviation D_(ilx) is low.

10. The conditional proposition (P10→Q10) is such that, in the i-thsample shot area, (P10) if the reticle mark deviation ΔRS_(ily) is notequal to zero (=0), (Q10) the certainty W_(i10) of the detectedpositional deviation D_(ily) is low.

11. The conditional proposition (P11→Q11) is such that, in the i-thsample shot area, (P11) if the reticle mark deviation ΔRS_(irx) is notequal to zero (=0), (Q11) the certainty W_(i11) of the detectedpositional deviation D_(irx) is low.

12. The conditional proposition (P12→Q12) is such that, in the i-thsample shot area, (P12) if the reticle mark deviation ΔRS_(iry) is notequal to zero (=0), (Q12) the certainty W_(i12) of the detectedpositional deviation D_(iry) is low.

Also, the conditional propositions (P13→Q13) and (P14→Q14) relate to theshot magnification error ΔMag_(i) and the shot rotational angle errorΔθi, respectively, discussed in items (4) and (5). More specifically:

13. The conditional proposition (P13→Q13) is such that, in the i-thsample shot ares, (P13) if the shot magnification error ΔMag_(i) is notequal to zero (=0), (Q13) the certainty W_(i13) of the detectedpositional deviations D_(ix) and D_(iy) is low.

14. The conditional proposition (P14→Q14) is such that, in the i-thsample shot area, (P14) if the shot rotational angle error Δθi is notequal to zero (=0), (Q14) the certainty W_(i14) of the detectedpositional deviations D_(ix) and D_(iy) is low.

By using linguistic truth values related to the fuzzy reasoning, theconditional proposition (P1→Q1), for example, of the above-describedconditional propositions (Pj-Qj), can be expressed as follows:

(A) if P_(ilx) is BG then W_(i1) is GD.

(B) if P_(ilx) is MD then W_(i1) is UK.

(C) if P_(ilx) is SM then W_(i1) is NG.

Here, the abbreviations "BG", "MD" and "SM" correspond to the linguistictruth values of the antecedent propositions, respectively, and they arefuzzy sets which mean "big", "middle" and "small", respectively. Also,the abbreviations "GD", "UK" and "NG" correspond to the linguistic truthvalues of the consequent propositions, respectively, and they are fuzzysets which mean "good", "unknown" and "no good", respectively. Further,while not described in detail, the conditional propositions (P2→Q2),(P3→Q3) and (P4→Q4) can be expressed similarly by using the linguistictruth values.

Also, the conditional proposition (P5→Q5) can be expressed by using thelinguistic truth values related to the fuzzy reasoning, in the followingmanner:

(A) if σ_(ilx) is SM then W_(i5) is GD.

(B) if σ_(ilx) is MD then W_(i5) is UK.

(C) if σ_(ilx) is BG then W_(i5) is NG.

Similarly, the abbreviations "BG", "MD" and "SM" correspond to thelinguistic truth values of the antecedent propositions, respectively,and they are fuzzy sets which mean "big", "middle" and "small",respectively. Also, the abbreviations "GD", "UK" and "NG" correspond tothe linguistic truth values of the consequent propositions,respectively, and they are fuzzy sets which mean "good", "unknown" and"no good", respectively. Further, while not described in detail, theconditional propositions (P6→Q6), (P7→Q7) and (P8→Q8) can be expressedsimilarly by using the linguistic truth values.

Further, by using the linguistic truth values related to the fuzzyreasoning, the conditional proposition (P9→Q9) can be expressed asfollows:

(A) if ΔRS_(ilx) is NB then W_(i9) is NG.

(B) if ΔRS_(ilx) is NS then W_(i9) is UK.

(C) if ΔRS_(ilx) is ZE then W_(i9) is GD.

(D) if ΔRS_(ilx) is PS then W_(i9) is UK.

(E) if ΔRS_(ilx) is PB then W_(i9) is NG.

Here, the abbreviations "NB", "NS", "ZE", "PS" and "PB" correspond tothe linguistic truth values of the antecedent propositions,respectively, and they are the fuzzy sets which mean "negative big","negative small", "zero", "positive small" and "positive big". Also, theabbreviations "GD", "UK" and "NG" correspond to the linguistic truthvalues of the consequent propositions, respectively, and they are thefuzzy sets which mean "good", "unknown" and "no good". Further, whilenot described in detail, the conditional propositions (P10→Q10),(P11→Q11), (P12→Q12), (P13→Q13) and (P14→Q14) can be expressed in asimilar manner, by using the linguistic truth values.

The respective fuzzy sets of the linguistic truth values (SM, MD andBG), (NB, NS, ZE, PS and PB) (GD, UK and NG) of the conditionalpropositions (Pj→Qj) are determined as different sets, in accordancewith empirical rules of each conditional proposition (Pj→Qj), and theyare set into a memory of the characteristic parameter extracting device24 in the form of membership functions, by an operator and through theconsole CS (FIG. 1).

Also, in response to instructions by the operator from the console CS,the characteristic parameter extracting device 24 operates to make aselection for the conditional propositions (Pj→Qj) to be used todetermine the certainty W_(ix) and W_(iy) of the detected positionaldeviation D_(ix) and D_(iy) of the i-th sample shot area SSi. Forexample, the characteristic parameter extracting device 24 selects allthe conditional propositions (Pj→Qj) or a part of these conditionalpropositions, for determination of the certainty W_(ix) and W_(iy).While such selection is determined by the operator beforehand, differentselections may be made for different sample shot areas SSi, differentwafers WF or different lots of wafers WF, depending on the position ofeach sample shot area SSi of each wafer WF, the shape of each mark, thetype or state of each resist applied.

Next, the manner of determining the certainty W_(ix) and W_(iy) by thecharacteristic parameter extracting device 24 will be explained, withreference to an example wherein all the conditional propositions (Pj→Qj)described above are used. Here, if the consequent propositions of thecertainty W_(ix) and W_(iy) (determined or defined value which is not afuzzy numeral but a crisp value) of the detected positional deviationD_(ix) and D_(iy) of the i-th sample shot area SSi are denoted by Q_(ix)and Q_(iy) (fuzzy sets), then for each sample shot area SSi thecharacteristic parameter extracting device 24 performs the fuzzyreasoning based on the V-operation so as to provide:

(P₁ V P₂ V P₅ V P₆ V P₉ V P₁₀ V P₁₃ V P₁₄)→Q_(ix)

(P₃ V P₄ V P₇ V P₈ V P₁₁ V P₁₂ V P₁₃ V P₁₄)→Q_(iy)

Namely,

Q_(ix) =(Q₁ V Q₂ V Q₅ V Q₆ V Q₉ V Q₁₀ V Q₁₃ V Q₁₄)

Q_(iy) =(Q₃ V Q₄ V Q₇ V Q₈ V Q₁₁ V Q₁₂ V Q₁₃ V Q₁₄)

Since the V-operation in the fuzzy set shows the MAX-operation (if, oftwo numerals a and b, a>b, then MAX {a, b}=a), the above equations canbe rewritten as follows:

Q_(ix) =MAX (Q₁,Q₂,Q₅,Q₆,Q₉,Q₁₀,Q₁₃,Q₁₄)

Q_(iy) =MAX (Q₃,Q₄,Q₇,Q₈,Q₁₁,Q₁₂,Q₁₃,Q₁₄)

Subsequently, the characteristic parameter extracting device 24 operatesto quantify the fuzzy sets Q_(ix) and Q_(iy) into the defined values ofcertainty W_(ix) and W_(iy). This quantification can be made bycalculating the gravity center of the membership functions of the fuzzysets Q_(ix) and Q_(iy).

That is, by taking Q_(ix) as the value on the coordinate q_(x) and bytaking the membership function as Q_(ix) =f(qx), the certainty iscalculated by: ##EQU11## Similarly, by taking Q_(iy) as the value on thecoordinate qy and by taking the membership function as Q_(iy) =f(qy),the certainty is calculated by: ##EQU12##

Then, the characteristic parameter extracting device 24 outputs thedefined values of certainty W_(ix) and W_(iy), as the characteristicparameters.

It is to be noted here that, if the defined values of the certaintyW_(ix) and W_(iy) are very small as compared with a certain preset valueand thus they are not effective, the characteristic parameter extractingdevice 24 produces a zero output in place of the defined values, tothereby avoid that the positional deviations D_(ix) and D_(iy)corresponding to that certainty are influential to the preparation of acorrected grid to be described later. In other words, it determines thecertainty W_(ix) and W_(iy) so as to allow rejection of what can becalled "extraordinary values" during the subsequent computation fordetermining the corrective grid. However, this is not limiting but maybe modified in response to instructions given by the operatorbeforehand, from the console CS. Also, it is possible to change thepreset value.

Next, the sequence of an alignment operation in this embodiment will beexplained with reference to the flow chart of FIG. 14.

Step S01

First, the reticle RT is introduced onto the reticle stage RS by meansof a conveying hand mechanism (not shown), and the reticle is fixedlyheld on the reticle stage by vacuum attraction. After this, theobjective mirrors AML and AMR are moved to the positions just above thereticle setting marks RSML and RSMR, respectively, which are in apredetermined positional relationship with the projection lens LN. Then,superposed images of the reticle setting mark RSML (RSMR) and thereticle alignment mark RAML (RAMR) provided on the reticle RT, arepicked up by the image pickup device CM. The control unit CU processesthe image data (video signal) from the image pickup device CM andcalculates the relative positional deviation, i.e., the positionaldeviation of the reticle RT with respect to the projection lens LN.Then, the control unit CU controllably moves the reticle stage RS in theX, Y and/or θ direction to reduce the positional deviation to zero. Bythis, the reticle RT can be brought into a predetermined positionalrelationship with the projection lens LN.

Step S02

Then, the wafer WF is introduced onto the wafer stage WS by means of aconveying hand mechanism (not shown), and the wafer is fixedly held onthe wafer stage by vacuum attraction. Since the wafer has beenprealigned, the disposition of the shot areas SH thereon when the waferis introduced onto the wafer stage WS is approximately in a parallelrelationship with the X and Y directions in the X-Y coordinates. Also,the center of the wafer is approximately coincident with the center ofthe wafer stage WS. The design disposition data of the shot areas SH aswell as the position data of the wafer alignment marks WAML and WAMRhave been memorized into a memory of the control unit CU, from theconsole CS. Thus, the control unit CU can control the movement of theX-Y stage XYS in the X and Y directions on the basis of the positionaldata of the X-Y stage in the X and Y directions as measured through thelaser interferometers IFX and IFY, by which each shot area SH of thewafer WF can be approximately positioned below the projection lens LNand, also, each of the wafer alignment marks WAML and WAMR can beapproximately positioned below the off-axis scope OS.

The operation to be performed at Steps S03 and S04 is an operation foraligning the wafer WF as a whole with a relatively low precision. Thisis a preliminary operation to the high-precision alignment measurementto be made at Steps S05-S12 and can be omitted provided that theprealignment operation has a sufficient precision. Generally, however,it is necessary.

Step S03

First, on the basis of the positional data of the X-Y stage XYS measuredthrough the interferometers IFS and IFY as well as the design positionaldata of the wafer alignment mark WAML, the control unit CU controls themovement of the X-Y stage XYS in the X and Y directions so that thewafer alignment mark WAML comes to the position just below the off-axisscope OS. Then, an image of the wafer alignment mark WAML is picked upthrough the off-axis scope OS. The position of the thus picked-up imageof the wafer alignment mark WAML is displaced from the center of theimage-taking picture plane of the off-axis scope OS by an amountcorresponding to the inaccurateness of the wafer WF placement withrespect to the wafer stage WS. From the image data produced by theoff-axis scope OS, the control unit CU calculates the amount of suchdisplacement (deviation) and memorizes it into the memory thereof.

Subsequently, through similar movement of the X-Y stage XYS, the otherwafer alignment mark WAMR is positioned just below the off-axis scopeOS, and the image thereof is picked up through the off-axis scope OS.Any positional deviation thereof is calculated and recorded by thecontrol unit CU.

Step S04

From the obtained positional deviations of the wafer alignment marksWAML and WAMR, measured at step S03, deviations of the wafer WF from itsdesign position with respect to the X, Y and θ directions arecalculated. The deviation in the θ direction (rotational error) iscorrected by rotationally moving the wafer stage WS in the θ direction.The deviation in the X direction is recorded as a shift componentvariable Sx while the deviation in the Y direction is recorded as ashift component variable Sy. Also, at this time, the magnificationcomponent variables βx and βy in the X and Y directions as well as therotational component variables θx and θy are all initialized to zero.

These variables Sx, Sy, βx, βy, θx and θy are used at Steps S07 and S09(to be described) for determination of corrective values (correctedgrating) to the design disposition data of the shot areas SH.Hereinafter, they are also used in a combined form of components ofvectors A and S, such as follows: ##EQU13##

Steps S05-S08 and Steps S09-S12 are the main part of the aligning methodaccording to the present invention. While similar processings areperformed at Steps S05-S08 and at Steps S09-S12, the operations to bemade at Steps S05-S08 are those to be made when the number of sampleshot areas to be selected as the subject of measurement is reduced (forexample, only four preparatory sample shot areas SS1, SS3, SS5 and SS7shown in FIG. 3 are selected) so as to obtain a medium alignmentprecision without expense of a long time. On the other hand, theoperations to be made at Steps S09-S12 are those to be made when thenumber of sample shot areas to be selected as the subject of measurementis increased (for example, eight main sample shot areas SS1-SS8 in FIG.3 are selected) so as to obtain high alignment precision. The alignmentoperation is repeated step by step because there is a tendency that theprecision of deviation measurement is not so good when the amount ofdeviation is large and it is considered that the precision can beenhanced by reducing the deviation to zero step by step.

Step S05

At this step, positional deviations of the preparatory sample shot areasSS1, SS3, SS5 and SS7 of FIG. 3, are measured in accordance with thesequence shown in the flow chart of FIG. 15. Details of this operationwill be explained with reference to FIG. 15.

Step S101

First, the variable i (i=1-n where n is the number of the preparatorysample shot areas) is set to be equal to 1. Character "i" denotes avariable representing the ordinal number of that sample shot area and,hereinafter, it is used as a suffix when particular data different foreach sample shot area is to be expressed.

Step S102

In the X-Y coordinates, a vector Pi representing the design position ofthe i-th sample shot area (see FIG. 16) is expressed as: ##EQU14## and,from the vectors A and S obtained at step S04 described above, a vectorqi representing the measuring position (FIG. 16) is detected inaccordance with the following equation:

    q.sub.i =Pi+APi+S

Then, in accordance with this measuring position q_(i), the movement ofthe X-Y stage XYS in the X and Y directions is controlled. In otherwords, the X-Y stage XYS movement is controlled so that the positionrepresented by q_(i) in the X-Y coordinates having an origin O at theoptical axis position of the projection lens LN becomes coincident withthe optical axis position of the projection lens LN. As a result of suchmovement, the i-th sample shot area can be placed at the deviationmeasuring position with a smaller error than on an occasion when it ismoved to the design position Pi. As described hereinbefore, the designposition Pi has been inputted into the control unit CU beforehand, fromthe console CS.

Step S103

Then, superposed images of the wafer marks WML_(x), WML_(y), WMR_(x) andWMR_(y) of the i-th sample shot area on the wafer WF and the reticlemarks RML_(x), RML_(y), RMR_(x) and RMR_(y) on the reticle RT (see FIG.4), are picked up through the image pickup device CM, and the image datafrom the image pickup device CM at this time is processed by the controlunit CU, whereby various data related to the i-th sample shot area areproduced. More specifically, as described, the position detecting device23 in FIG. 2 calculates the positional deviations D_(ilx), D_(ily),D_(irx) and D_(iry), while the characteristic parameter extractingdevice 24 calculates the peak match degrees P_(ilx), P_(ily), P_(irx)and P_(iry), the variances σ_(ilx), σ_(ily), σ_(irx) and σ_(iry) of themeasured values, the reticle mark deviations ΔRS_(ilx), ΔRS_(ily),ΔRS_(irx) and ΔRS_(iry), the shot magnification error ΔMag_(i) and theshot rotational angle error Δθi.

If the shot area SH position on the wafer WF. is exactly at the designvalue Pi and the wafer alignment operation at Steps S03 and S04 has beenaccomplished idealistically accurately, naturally at this moment thewafer marks WML_(x), WML_(y), WMR_(x) and WMR_(y) of the sample shotarea, which is the subject of measurement at this moment should besuperposed upon corresponding reticle marks RML_(x), RML_(y), RMR_(x)and RMR_(y) each accurately in a predetermined positional relationship.Actually, however, there are positional deviations produced as a resultof deformation of the wafer WF, a remainder of wafer alignment and thelike.

Step S104

Various data of the i-th sample shot area obtained at the step S103 arerecorded into variables such as set forth below, to allow reference atStep S06 and S07 (or Steps S10 and S11) to be described later:

Positional Deviation:

D_(ilx) =D_(lx), D_(ily) =D_(ly)

D_(irx) =D_(rx), D_(iry) =D_(ry)

Reticle Mark Spacing:

RS_(ilx) =RS_(lx), RS_(ily) =RS_(ly)

RS_(irx) =RS_(rx), RS_(iry) =RS_(ry)

Peak Match Degree:

P_(ilx) =P_(lx), P_(ily) =P_(ly)

P_(irx) =P_(rx), P_(iry) =P_(ry)

Variance of Measured Values:

σ_(ilx) =σ_(lx), σ_(ily) =σ_(ly)

σ_(irx) =σ_(rx), σ_(iry) =σ_(ry)

Shot Magnification Error:

ΔMag_(i) =ΔMag

Shot Rotational Angle Error:

Δθ_(i) =Δθ

Also, by taking the positional deviation of the center of the i-thsample shot area as a vector M_(i) (see FIG. 16) and by taking themeasured shot position as a vector t_(i) (FIG. 16), the following isset:

Center Deviation: ##EQU15## Step S105

For the measurement to the next sample shot area, the variable i isincremented by one (1).

Step S106

Until the measurement to all the sample shot areas SSi (at step S05, thenumber n of the preparatory sample shot areas shown in FIG. 3 is n=4) iscompleted, Steps S102-S105 are repeated while moving the X-Y stage XYSin the X and Y directions on the basis of the measured position q_(i) asdescribed. At Step S105, this measurement is repeatedly performed fourtimes and, thereafter, the sequence goes to Step S06 in FIG. 14.

Step S06 Here, by using various data obtained at Step S05, thecharacteristic parameter extracting device 24 determines the certaintyW_(ix) (W_(iy)) of the positional deviation D_(ix) (D_(iy)) of thecenter of each sample shot area. This can be determined in the manner asdescribed hereinbefore, and here it is not explained again.

Step S07

After the certainty W_(ix) and W_(iy) is obtained, in order to determinethe corrected position q_(i) shown in FIG. 16, namely, in order todetermine the position with which the movement of the X-Y stage XYS isto be controlled for step-and-repeat printing of the reticle pattern RTonto each shot area SH of the wafer WF, the control unit CU freshlycalculates the following corrected values AS by using the measuredposition t_(i) of each sample shot area and the designed position Pi ofeach sample shot area. That is: ##EQU16## While these corrected values Aand S can be calculated in many ways in the present embodiment they arecalculated as follows:

Namely, on an assumption that the corrected position q_(i) is to beapproximated with a linear function, q_(i) is expressed by:

    q.sub.i =Pi+APi+S

and the remainder r_(i) to the measured position t_(i) (see FIG. 16)when correction is made with the corrected position q_(i) is expressedby: ##EQU17## Then, the corrected values A and S are so determined thatthe sum of the squares of the remainders r_(ix) and r_(iy) weightedrespectively with respective certainties W_(ix) and W_(iy), becomesminimum. The meaning of the certainty W_(ix) and W_(iy) is such asdescribed hereinbefore, and it is determined so that a measured positiont_(i) having a high reliability is more influential to the correctedposition (corrected grating) q_(i). As described, a measured position(positional deviation) t_(i) always contains a measurement error due to,for example, the mark configuration, the state of the applied resist andthe expansion/contraction of the wafer WF. Also, for each sample shotarea, the measurement error is different. Accordingly, if the correctedposition q_(i) (i.e., the corrected values A and S) is simply determinedso as to minimize the sum of the squares of the remainders r_(i), thecertainty of the corrected position q_(i) reduces correspondingly to therandom measurement error contained in each measured position t_(i)although the measurement error may be canceled to some extent by theleast square method.

In consideration thereof, by weighting with the certainty W_(ix) andW_(iy), the control unit CU defines an evaluated quantity V such as:##EQU18## and determines the corrected values A and S so that thequantity V becomes minimum. That is: ##EQU19## βx, βy, θx, θy, Sx and Syare calculated accordingly.

Here, if the deviation from the designed position Pi of the sample shotarea is denoted by: ##EQU20## then,

    r.sub.i =AP.sub.i +S-d.sub.i

(as regards the relationship of the vectors, see FIG. 16)

Accordingly, the above-described evaluated quantity V can be rewrittenas: ##EQU21## wherein ##EQU22##

It follows therefrom that ∇V=0 is rewritten by: ##EQU23## By solvingthis, the following is obtained:

    β.sub.x ={D.sub.xxx (C.sub.xyy C.sub.x -C.sub.xy.sup.2)+D.sub.xxy (C.sub.xy C.sub.xx -C.sub.xxy C.sub.x)+D.sub.xx (C.sub.xxy C.sub.xy -C.sub.xyy C.sub.xx)}/det.sub.x

    β.sub.y ={D.sub.yyy (C.sub.yxx C.sub.y -C.sub.yx.sup.2)+D.sub.yyx (C.sub.yx C.sub.yy -C.sub.yyx C.sub.y) +D.sub.yy (C.sub.yyx C.sub.yx -C.sub.yxx C.sub.yy)}/det.sub.y

    θ.sub.x ={D.sub.yyx (C.sub.yyy C.sub.y -C.sub.yy.sup.2)+D.sub.yyy (C.sub.yx C.sub.yy -C.sub.yyx C.sub.y)+D.sub.yy (C.sub.yyx C.sub.yy -C.sub.yyy C.sub.yx)}/det.sub.y

    θ.sub.y ={D.sub.xxy (C.sub.xxx C.sub.x -C.sub.xx.sup.2)+D.sub.xxx (C.sub.xy C.sub.xx -C.sub.xxy C.sub.x)+D.sub.xx (C.sub.xxy C.sub.xx -C.sub.xxx C.sub.xy)}/det.sub.x

    S.sub.x ={D.sub.xx β.sub.x -C.sub.xy θ.sub.y }/C.sub.x

    S.sub.y ={D.sub.yy -C.sub.yy β.sub.y -C.sub.yx θ.sub.x }/C.sub.y

wherein,

det_(x) =C_(xxx) C_(xyy) C_(x) +2C_(xxy) C_(xx) C_(xy) -C_(xxx) C_(xy) ²-C_(xyy) C_(xx) ² -C_(x) C_(xxy) ²

det_(y) =C_(yyy) C_(y) +2C_(yyx) C_(yx) -C_(yyy) C_(yx) ² -C_(yxx)C_(yy) ² -C_(y) C_(yyx) ²

The corrected values A and S are determined in this manner and they areused later at Step S09 to calculate again the sample shot measuringposition q_(i).

Subsequently, the control unit CU calculates the amount of rotationaldrive (θc) of the reticle stage RS for correction of the chip rotation.To this end, the amount of chip rotation (θi) is expressed by using thewafer mark span MS (see FIG. 3), as follows:

    θi=(D.sub.iry -D.sub.ily)/MS

Then, while taking into consideration the certainty W_(iy) in the Ydirection, the rotational driving amount is determined as follows:##EQU24## Step S08

The reticle stage RS is rotationally moved in the θ direction by anamount θc (rotational driving amount) as obtained at Step S07, to adjustthe chip rotation.

Subsequently, the number of sample shot areas SSi is increased to eight(i.e., the main sample shot areas SS1-SS8 of FIG. 3) and Steps S09-S12similar to Steps S05-S08 are performed. Except for an increased number nof the sample shot areas, basically the Steps S09-S12 are the same asSteps S05-S08, such that they will be explained here briefly.

Step S09

While moving the X-Y stage XYS by using the measurement position q_(i),the positional deviation of the main sample shot area SSi (i=1-8) ismeasured. The measurement position q_(i) at this time is determined byusing the corrected values A and S obtained at Step S07 as well as thedesigned position Pi. It is to be noted here that, at this step, withregard to the sample shot area SS1, SS3, SS5 and SS7 of all the selectedsample shot areas SSi (i=1-8), the positional deviation has already beenmeasured at Step S05 and, therefore, the measurement may not beperformed again and the already obtained positional deviation may beused.

Step S10

The characteristic parameter extracting device 24 calculates thecertainty W_(ix) and W_(iy) of the measured positional deviation of eachsample shot area.

Step S11

Then, the corrected values A and S for determining the correctedposition (corrected grating) q_(i) is determined from the measuredpositional deviations of the eight sample shot areas and theircertainties. Also, the amount of rotational drive (θc) of the reticlestage RS is calculated.

Step S12

The reticle stage RS is rotationally moved in the θ direction by anamount θc (rotationally driving amount) as determined at Step S11.

With the foregoing operations, the determination of the correctedposition (corrected grating) q_(i) of each shot area SH of the wafer WFis completed and, thereafter, while moving the X-Y stage XYS stepwise inaccordance with the thus determined corrected grating (correctedcoordinates), the pattern PT provided on the reticle RT is printed oneach shot area SH.

Step S13

From the corrected values A and S obtained at Step S11 as well as thedesigned position Pi, the corrected position q_(i) is determined asfollows:

    q.sub.i =Pi+APi+S

and the movement of the X-Y stage XYS is controlled on the basis of thethus determined position q_(i), whereby the i-th shot area SH ispositioned exactly below the projection lens LN. Subsequently, theshutter SHT is opened to start the exposure with the printing light fromthe exposure light source IL, whereby the pattern of the reticle RT isprinted on the i-th shot area SH through the projection lens LN. As theamount of exposure becomes equal to a predetermined amount (this valuehas been inputted in preparation into the control unit from the consoleCS), the shutter SHT is closed whereby the exposure of the i-th shotarea SH is completed. Then, until the exposures of all the shot areas onthe wafer WF are completed, the movement of the X-Y stage XYS based onthe corrected position q_(i) and the exposure operation are repeated.

Step S14

The wafer WF having its exposure completed is unloaded from the waferstage WS by means of a conveying hand mechanism (not shown) and isstored into a wafer carrier (not shown).

Step S15

Steps S02-S15 are repeated until the exposure operation to all thewafers to be processed is completed.

With the operation described above, the alignment operation according tothe present invention is completed.

Although the present invention has been explained in the foregoing to anembodiment wherein the positional deviation of each shot area SH of awafer WF with respect to a reticle RT is detected by using reticle marksRML and RMR provided on the reticle RT and wafer marks WML and WMRprovided on the wafer WF, as a matter of course the present invention isapplicable also to a case wherein the position of each shot area ismeasured in a different method.

FIG. 17 shows a major part of a step-and-repeat type exposure apparatus,which is another example embodying the present invention and having adifferent arrangement for measuring the position of each shot area on awafer WF. In FIG. 17, laser light from a light source LS is divided by abeam splitter BS into two optical paths and thereafter, from objectivemirrors Mx and My disposed between a reticle stage RS and a projectionlens LN, they are projected to the projection lens LN to illuminatewafer marks WMx and WMy provided on the wafer WF. Image pickup deviceCMx is provided to pick up an image of the wafer mark WMx through theprojection lens LN, the objective mirror Mx and a half mirror HMx, whileanother image pickup device CMy is provided to pick up an image of thewafer mark WMy through the projection lens LN, the objective mirror Myand a half mirror HMy. In this example, the positional deviation of thewafer mark WMx (WMy) is detected with respect to a predeterminedreference position set in relation to the image pickup device CMx (CMy)such as, for example, the image pickup surface of the image pickupdevice CMx (CMy).

Also, in this example, provided that the positional relationship betweenthe above-described reference position and the reticle RT held by thereticle stage RS is maintained with sufficient precision at a knownvalue, the present invention is applicable similarly. Also, while in theembodiment described hereinbefore the positional deviation of each shotarea is detected and the measuring position q_(i) of each shot area isdetermined from the detected deviation and the designed position Pi ofeach shot area, the measuring position may be determined directly fromthe values measured through the laser interferometers IFX and IFY, forexample. On that occasion, the measurement position to each shot area SHmay be determined from the values obtained through the laserinterferometers IFX and IFY when attainment of a predeterminedpositional relationship between the reticle mark and the wafer mark isdiscriminated on the basis of the video output from the image pickupdevice CM. Also, in the example of FIG. 17, it may be determined fromthe measured values of the laser interferometers IFX and IFY whencoincidence of the wafer mark with the above-described referenceposition is discriminated on the basis of the video outputs of the imagepickup devices CMx and CMy.

Further, while in the foregoing embodiments description has been made toan example wherein each mark is detected by using an image pickupdevice, the present invention is also applicable to a system having aphotodetector such as disclosed in the aforementioned Japanese Laid-OpenPatent Application, Laid-Open No. Sho 63-232321, for example. On thatoccasion, the certainty W_(ix) and W_(iy) may be determined by using asan evaluated quantity the waveform of a mark signal outputted from thephotodetector. Further, the measurement of the position of each shotarea SH by using wafer marks may be made without intervention of theprojection lens LN. For example, a separate microscope which is held ina particular positional relationship with the projection lens LN atsufficient precision, such as an off-axis scope OS, may be used. On thatoccasion, the present invention is also applicable to the concept ofwhat can be called a "latent image alignment" such as disclosed inJapanese Laid-Open Patent Application, Laid-Open No. Sho 61-114529, forexample.

Further, while in the foregoing embodiments the certainty W_(ix) andW_(iy) is determined in accordance with the fuzzy reasoning, this may bedetermined in accordance with a different, more common method. As anexample, if the conditional propositions (Pi→Qi) are defined as:

    Qi=f.sub.i (Pi)

where

    i=1-n

and if, by using a method such as the multivariate analysis or the like,the factors of the conditional propositions of a number n are determinedas a₁ -a_(n), respectively, then it is possible to determine thecertainty W_(ix) and W_(iy) from the various data as described, inaccordance with the linear additive association method or the linearmultiplicative association method, for example.

In the case of linear additive association, assuming that thecoefficient of the conditional proposition (Pi→Qi) for determining thecertainty W_(ix) is represented by a_(i) (i=1-n) and that theconditional proposition (Pi→Qi) is represented by

    Qi=f.sub.i (Pi),

then, the certainty W_(ix) may be determined as follows:

    W.sub.ix =a.sub.1 ·f.sub.1 +a.sub.2 ·f.sub.2 + . . . +a.sub.i ·f.sub.i + . . . +a.sub.n ·f.sub.n

Also, assuming that the coefficient of the conditional proposition(Pi→Qi) for determining the certainty W_(iy) represented by b_(i)(i=1-m) and that the conditional proposition (Pi→Qi) is represented by:

    Qi=g.sub.i (Pi),

then, the certain W_(iy) may be determined as follows:

    W.sub.iy =b.sub.i ·g.sub.i +b.sub.2 ·g.sub.2 + . . . +b.sub.i ·g.sub.i + . . . +b.sub.m ·g.sub.m

In the case of linear multiplicative association, similarly they may bedetermined as follows:

    W.sub.ix =a.sub.1 ·f.sub.1 ·a.sub.2 ·f.sub.2 . . . a.sub.i ·f.sub.i . . . a.sub.n ·f.sub.n

    W.sub.iy =b.sub.1 ·g.sub.1 ·b.sub.2 ·g.sub.2 . . . b.sub.i ·g.sub.i . . . b.sub.m ·g.sub.m

Also, if only one conditional proposition (Pi→Qi) is sufficient fordetermination of each of the certainty W_(ix) and the certainty W_(iy),they can be determined more simply. That is:

    W.sub.ix =f(Pi)

    W.sub.iy =g(Pi)

Further, while in the foregoing embodiments the calculation of thecorrected position q_(i) of each shot area (namely, the corrected valuesA and S for determining the corrected coordinates (corrected grating))is determined so as to make minimum the sum of the squares of theremainders r_(ix) and r_(iy) weighted with the certainty W_(ix) andW_(iy), this may be determined so as to make minimum the sum of theabsolute values of the remainders r_(ix) and r_(iy) weighted with thecertainty W_(ix) and W_(iy). Namely, an evaluated quantity E_(abs) maybe defined as: ##EQU25## and the values A and S which are given by:##EQU26## and which make E_(abs) minimum, may be determined.

Since the function E_(abs) has a singular point, differentiation is notpossible. For this reason, the analytic method such as described withreference to Step S07 in the preceding embodiment cannot be definedsatisfactorily. Accordingly, on this occasion, the function E_(abs) isconsidered as a function defined in a six-dimensional parameter space(βx, βy, θx, θy, Sx and Sy) and the vector Φ.tbd.(βx, βy, θx, θy, Sx andSy) on the six-dimensional space is deflected in a trial-and-errormanner, and Φ_(solv) that makes E_(abs) minimum is determined.

A basic concept of the determination of such Φ_(solv) will be explainedbelow. For simplicity in explanation, the above-described Φ is definedas:

    Φ.tbd.(φ.sub.1, φ.sub.2, φ.sub.3, φ.sub.4, φ.sub.5, φ.sub.6)

     .tbd.(x, y, θx, θy, Sx, Sy)

and the evaluation function E_(abs) is set as E_(abs) =E_(abs) (Φ).Further, the unit vector as defined by Φ is represented by ε_(u) (u=1,2, 3, 4, 5 and 6). Here, as an example:

    β.sub.x ε.sub.1 =(βx, 0, 0, 0, 0, 0)

First, as an initial value, Φ₀ ⁰ is given. While changing the vector Φ₀⁰ in the φ₁ axis direction (βx direction) by δ₁ ⁰, such δ₁.sup. thatmakes E_(abs) minimum is set as δ₁ ⁰, where

    E.sub.abs =E.sub.abs (Φ.sub.0.sup.0 +δ.sub.1.sup.0 ε.sub.1)

and the vector value Φ₀ ⁰ is taken as the vector value Φ₁ ⁰. Here,

    Φ.sub.1.sup.0 =Φ.sub.0.sup.0 +δ.sub.1.sup.0 ε.sub.1

Subsequently, as regards

    E.sub.abs =E.sub.abs (Φ.sub.1.sup.0 +δ.sub.2.sup.0 ε.sub.2)

while changing δ₂ ⁰, the vector value that makes E_(abs) is taken as Φ₂⁰. In this manner, with regard to the φ_(u) axes in sequence, such Φ_(u)⁰ that makes the function E_(abs) minimum is determined, and Φ₆ ⁰determined with respect to the φ₆ axis direction is defined again as Φ₀¹ (.tbd.Φ₁ ⁰). Then, the φ₁ axis is deflected again, and the vectorvalue that makes E_(abs) minimum is taken as Φ₁ ¹, where

    E.sub.abs =(Φ.sub.0.sup.1 δ.sub.1.sup.1 ε.sub.1)

In this manner, the vector values fur (u=1-6, r=0, 1, 2, . . . ) thatmakes E_(abs) minimum are determined in sequence, where

    E.sub.abs =(Φ.sub.u-1.sup.r +δ.sub.u.sup.r ε.sub.u)

Here, Φ₀ ^(r) .tbd.Φ₆ ^(r-1).

In actual calculation, δ_(u) ⁰ is placed with sufficiently roughprecision, while δ_(u) ^(R) has a precision increasing with the increaseof the suffix R. Finally, Φ₆ ^(r) as obtainable when the precision ofδ_(u) ¹ becomes equal to or higher than one required, is taken as asolution I_(solv).

Such a method of determination will be explained with reference to theflow chart of FIG. 18. At Step S201, an initial value for the parameterm that represents the degree of precision to be enhanced when the "R" isto be increased and also that represents the degree of deflection of thesix-dimensional vector Φ as well as an initial value for δ_(u) thatrepresents the roughness of δ_(u) ⁰, are given. At Step S202, an initialvalue of the six-dimensional vector Φ is determined. For reasonablecalculation, it is desirable that the initial value is close to thesolution. To this end, the initial value is determined by using theequations as illustrated in the block of Step S202. The variables inthese equations are defined in the chart given in the block of StepS202. Thereafter, in the loop corresponding to the change of the "R", Φ₆^(R) having higher precision is calculated and, if the precision issufficient, after discrimination at Step S204 the sequence goesoutwardly to Step S210. Of the loops, the loop comprising the StepsS205-S208 is the one for the "u". Then the aforementioned Φ₆ ^(r) isdetermined. The precision is enhanced and Φ₀ ^(r+1) =Φ₆ ^(r) isobtained. This is made at Step S209. The components of the thus obtainedΦ_(solv) are set as the corrected values A and S.

Further modified embodiments will be explained.

While in the preceding embodiment the corrected position q_(i) isapproximated with a linear function, this may be approximated with anon-linear function. For example, it is known that the disposition ofshot areas on a wafer having been exposed with a certain type of mirrorprojection aligner can be approximated with a certain non-linearfunction (e.g. Japanese Laid-Open Patent Application, Laid-Open No. Sho59-27525). Accordingly, when the aligning method of the presentinvention is to be applied to such a wafer, further enhancement of thealignment precision is possible by using the non-linear function such asdisclosed in the aforementioned patent document, in place of the linearfunction as described hereinbefore. It is to be noted that, when theshot disposition is non-linear, in place of using the approximation withsuch a non-linear function, the wafer may be divided into plural zonesand the aligning method of the preceding embodiment may be applied toeach individual zone.

Further, while in the preceding embodiment the number of the sample shotareas is changed between Steps S05-S08 and Steps S09-S12 and the loopfor determining the corrected position q_(i) is performed twice, a largenumber of sample shot areas is initially used so that, with a singleloop, the corrected position q_(i) for the Step S13 may be determined.Alternatively, the number of the sample shot areas may be changedadditionally, so as to repeatedly execute the loop not less than threetimes. Further, while the number of the sample shot areas is four atStep S05 and eight at Step S09, the invention is not limited to suchnumbers and any other arbitrary number may be used. As a matter ofcourse, the position of the sample shot area SSi on the wafer is notlimited to that as shown in FIG. 3, but it may be set as desired. Theycan be set as desired with the input from the console CS.

Further, while in the preceding embodiment description has been made ofan example where the invention is applied to a semiconductor devicemanufacturing step-and-repeat type exposure apparatus, the invention isalso applicable to any other apparatus. For example, the invention isapplicable to an apparatus for directly drawing a pattern on each shotarea on a workpiece such as a semiconductor wafer, by use of an electronbeam, a laser beam or the like. Further, the invention is applicable toa wafer probe or the like to be used for the inspection of thecharacteristics of each chip pattern on a semiconductor wafer.Additionally, the invention is applicable to an apparatus other thanthat to be used in the manufacture of semiconductor devices. In summary,the invention is applicable to any apparatus provided that it isarranged to process or operate to each of different regions on an objectwhile moving the object in the step-and-repeat manner.

In accordance with the present invention, as described hereinbefore, thecorrected positional data related to the disposition of all the regionscan be determined under stronger influence by a measured positional datahaving higher reliability. Therefore, it is possible to align eachregion in the step-and-repeat manner, with higher precision.

While the invention has been described with reference to the structuresdisclosed herein, it is not confined to the details set forth and thisapplication is intended to cover such modifications or changes as maycome within the purposes of the improvements or the scope of thefollowing claims.

What is claimed is:
 1. An aligning method for sequentially positioningdifferent regions on a workpiece to a predetermined site, said methodcomprising the steps of:detecting marks provided on selected regions onthe workpiece to obtain corresponding mark signals and then measuringrespective positional data related to the positions or positional errorsof said selected regions, on the basis of the mark signals; detectingthe reliability of each measured positional data of a correspondingselected region, on the basis of the state of a corresponding marksignal or the state of that measured positional data; preparingcorrected positional data related to the disposition of all the regionson the workpiece by using the measured positional data of the selectedregions and design positional data of the selected regions, wherein, forpreparation of the corrected positional data, each measured positionaldata is weighted in accordance with the detected reliability thereofsuch that a measured positional data having higher reliability is moreinfluential to determine the corrected positional data; and controllingmovement of the workpiece, for sequential positioning of the differentregions on the workpiece to the predetermined site, on the basis of theprepared corrected positional data.
 2. An aligning method forsequentially positioning different regions on a workpiece to apredetermined site, said method comprising the steps of:detecting marksprovided on selected regions on the workpiece to obtain correspondingmark signals and then measuring respective positional data related tothe positions or positional errors of said selected regions, on thebasis of the mark signals; detecting the reliability of each measuredpositional data of a corresponding selected region, on the basis of thestate of a corresponding mark signal or the state of that measuredpositional data; determining weighting values for the respectivemeasured positional data of the selected regions, on the basis of thedetected reliabilities of the respective measured positional data;preparing corrected positional data related to the disposition of allthe regions on the workpiece by using the measured positional data ofthe selected regions, design positional data of the selected regions andthe determined weighting values; and controlling movement of theworkpiece, for sequential positioning of the different regions on theworkpiece to the predetermined site, on the basis of the preparedcorrected positional data.
 3. A method according to claim 2, whereineach weighting value is selected out of a predetermined numerical rangeincluding zero.
 4. An aligning method for sequentially positioningdifferent regions on a workpiece to a predetermined site, said methodcomprising the steps:detecting images of marks provided on selectedregions on the workpiece through image pickup means having windows toobtain corresponding image signals from the windows, and then measuringrespective positional data related to the positions or positional errorsof the selected regions on the basis of the image signals; determiningweighting values indicative of reliability for the respective measuredpositional data of the selected regions, on the basis of the respectivestates of the image signals or of the respective states of the measuredpositional data of the selected regions; preparing corrected positionaldata related to the disposition of all the regions on the workpiece byusing the measured positional data of the selected regions, designpositional data of the selected regions and the determined weightingvalues; and controlling movement of the workpiece, for sequentialpositioning of the different regions on the workpiece to thepredetermined site, on the basis of the prepared corrected positionaldata.
 5. A method according to claim 4, wherein the determination of theweighting values of the measured positional data uses variance in themark position as obtainable on the basis of the image signals from thewindows.
 6. An aligning method for sequentially positioning differentregions on a workpiece to a predetermined site, said method comprisingthe steps of:detecting marks provided on selected regions on theworkpiece through a projection lens, for projecting a pattern of anoriginal to each region on the workpiece, to obtain corresponding marksignals and then measuring respective positional data related to thepositions or positional errors of the selected regions, on the basis ofthe mark signals; determining weighting values indicative of reliabilityfor the respective measured positional data of the selected regions, onthe basis of the respective states of the mark signals or of therespective states of the measured positional data of the selectedregions; preparing corrected positional data related to the dispositionof all the regions on the workpiece by using the measured positionaldata of the selected regions, design positional data of the selectedregions and the determined weighting values; and controlling movement ofthe workpiece, for sequential positioning of the different regions onthe workpiece to the predetermined site, on the basis of the preparedcorrected positional data.